On a Generalized Difference Sequence Spaces of Fractional Order associated with Multiplier Sequence Defined by A Modulus Function

Let Γ(m) denotes the gamma function of a real number m∉{0,-1,-2,…}. Then the difference matrix Δ^α of a fractional order α is defined as (Δ^α v)_k=∑_i〖(-1)^i (Γ(α+1))/(i!Γ(α-i+1)) v_(k+i) 〗. Using the difference operator Δ^α, we introduce paranormed difference sequence spaces N_θ (Δ^α,f,Λ,p) and S_θ...

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Bibliographic Details
Published in:Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi 2020-10, Vol.24 (5), p.1105-1114
Main Author: YAYING, Taja
Format: Article
Language:English
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Summary:Let Γ(m) denotes the gamma function of a real number m∉{0,-1,-2,…}. Then the difference matrix Δ^α of a fractional order α is defined as (Δ^α v)_k=∑_i〖(-1)^i (Γ(α+1))/(i!Γ(α-i+1)) v_(k+i) 〗. Using the difference operator Δ^α, we introduce paranormed difference sequence spaces N_θ (Δ^α,f,Λ,p) and S_θ (Δ^α,f,Λ,p) of fractional orders involving lacunary sequence, θ; modulus function, f and multiplier sequence, Λ=(λ_k). We investigate topological structures of these spaces and examine various inclusion relations.
ISSN:2147-835X
2147-835X
DOI:10.16984/saufenbilder.744881